<< Chapter < Page Chapter >> Page >
void sfft_fcf16_hc(sfft_plan_t *p, const void *vin, void *vout) {   const SFFT_D *in = vin;  SFFT_D *out = vout;   SFFT_R r0_1,r2_3,r4_5,r6_7,r8_9,r10_11,r12_13,r14_15;    L_4_4(in+0,in+16,in+8,in+24,&r0_1,&r2_3,&r8_9,&r10_11);   L_2_4(in+4,in+20,in+28,in+12,&r4_5,&r6_7,&r14_15,&r12_13);   K_N(VLIT4(0.7071,0.7071,1,1),      VLIT4(0.7071,-0.7071,0,-0),       &r0_1,&r2_3,&r4_5,&r6_7);   K_N(VLIT4(0.9239,0.9239,1,1),      VLIT4(0.3827,-0.3827,0,-0),       &r0_1,&r4_5,&r8_9,&r12_13);   S_4(r0_1,r4_5,r8_9,r12_13,out+0,out+8,out+16,out+24);  K_N(VLIT4(0.3827,0.3827,0.7071,0.7071),       VLIT4(0.9239,-0.9239,0.7071,-0.7071),      &r2_3,&r6_7,&r10_11,&r14_15);   S_4(r2_3,r6_7,r10_11,r14_15,out+4,out+12,out+20,out+28);}
Hard-coded VL-2 size-16 FFT

Scalability

So far, hard-coded transforms of vector length 1 and 2 have been presented. On Intel machines, VL-1 can be used to compute double-precision transforms with SSE2, while VL-2 can be used to compute double-precisiontransforms with AVX and single-precision transforms with SSE. The method of vectorization presented in this chapter scales above VL-2, and has been successfully used to compute VL-4 single-precision transforms with AVX.

The leaf primitives were coded by hand in all cases; VL-1 required L_2 and L_4 , while VL-2 required L_2_2 , L_2_4 , L_4_2 and L_4_4 . In the case of VL-4, not all permutations of possible leaf primitive were required – only 11 out of 16 were needed for the transforms that were generated.

It is an easy exercise to code the leaf primitives for V L 4 by hand, but for future machines that might feature vector lengths larger than 4, the leaf primitives could be automatically generated (in fact, "Other vector lengths" is concerned with automatic generation of leaf sub-transforms at another level of scale).

Constraints

For a transform of size N and leaf node size of S ( S = 4 in the examples in this chapter), the following constraint must be satisfied:

N / V L S

If this constraint is not satisfied, the size of either VL or S must be reduced. In practice, VL and S are small relative to the size of most transforms, and thus these corner cases typically only occur for very small sized transforms. Such an example is a size-2 transform when V L = 2 and S = 4 , where in this case the transform is too small to be computed with SIMD operations and should be computed with scalar arithmetic instead.

Performance

Single-precision, SSE (VL-2)
Double-precision, SSE (VL-1)
Single-precision, AVX (VL-4)
Double-precision, AVX (VL-2)
Performance of hard-coded FFTs on a Macbook Air 4,2.

[link] shows the results of a benchmark for transforms of size 4 through to 1024 running on a Macbook Air 4,2. The speed of FFTW 3.3 running in estimate and patient modes is also shown for comparison.

FFTW running in patient mode evaluates a huge configuration space of parameters, while the hard-coded FFT required no calibration.

A variety of vector lengths are represented, and the hard-coded FFTs have good performance while N / V L 128 . After this point, performance drops off and other techniques should be used. The following sections use the hard-coded FFT as a foundation for scaling to larger sizes of transforms.

Questions & Answers

what is mutation
Janga Reply
what is a cell
Sifune Reply
how is urine form
Sifune
what is antagonism?
mahase Reply
classification of plants, gymnosperm features.
Linsy Reply
what is the features of gymnosperm
Linsy
how many types of solid did we have
Samuel Reply
what is an ionic bond
Samuel
What is Atoms
Daprince Reply
what is fallopian tube
Merolyn
what is bladder
Merolyn
what's bulbourethral gland
Eduek Reply
urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
onuoha Reply
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
Jeremiah
what is heart
Konadu Reply
how is urine formed in human
Konadu
how is urine formed in human
Rahma
what is the diference between a cavity and a canal
Pelagie Reply
what is the causative agent of malaria
Diamond
malaria is caused by an insect called mosquito.
Naomi
Malaria is cause by female anopheles mosquito
Isaac
Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
Olalekan
a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
Achor
how are lungs work
Commander
where does digestion begins
Achiri Reply
in the mouth
EZEKIEL
what are the functions of follicle stimulating harmones?
Rashima Reply
stimulates the follicle to release the mature ovum into the oviduct
Davonte
what are the functions of Endocrine and pituitary gland
Chinaza
endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
Achor
what's biology?
Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
Lisah
biology is the study of life.
Alfreda
Biology is the study of how living organisms live and survive in a specific environment
Sifune
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Computing the fast fourier transform on simd microprocessors. OpenStax CNX. Jul 15, 2012 Download for free at http://cnx.org/content/col11438/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Computing the fast fourier transform on simd microprocessors' conversation and receive update notifications?

Ask